I am not sure what universe you are in, but my experience with applying for an ESRC DTP studentship is that it couldn't be more straight-forward ( I am currently going through the process, and is waiting for a decision, due in Mid-March).

Once I had identified a suitable supervisor, I made contact, had an informal meeting which included discussion about funding once he agreed to supervisor my project. Was told to have all the documents ready by a certain date, which was forwarded to the institution's liaison for the DTP. Got reminder emails in November and December about the deadlines, relevant dates (internal review, Pathway review and then the final studentship committee decision) together with the application guidelines. It is ultra competitive from what they say, so the wait is most certainly stressful, but the application itself was very straight-forward. Transcripts, degree certificates, academic CV, references, proposal and completing a nomination form with the help of the supervisors. I'd say that it can't really be much simpler, especially when you consider that the funding amounts to over 70K over 3.5 years ( I am applying for a 3.5 studentship with 6 months of research methods).

I still don't know what you mean by being 'invited' to make an application. Being 'invited' implies that you only have to apply to get the funding. That being the case, I really don't see where you might have a problem. If 'invited' means that someone (your supervisor/ DTP/ESRC) told you that you can apply for studentships via the DTP, then 'invited' is probably not a good term.

As for the chance of success, it depends on which DTP you are applying to, the number and strength of this year's applicants, your field and of course, the strength of your application, of which your academic records (plus references) account for only about 33% of the marking criteria.

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Words have power. The way the discourse is being conducted can shape our outlook of the world, hence it is never acceptable to use discriminatory terms, that is of course, unless we wish to be discriminatory.

I think applications will be opened in the Spring (whatever that means, perhaps March-April?), for students starting a PhD course in the 2018 academic year (Sept/Oct 2018).

If you are due to start in Feb, it might be an idea to defer your start until Sept if you really need the loan to make ends-meet, as it is clearly stated that student already studying a PhD are not eligible for the loan.

I think its fine to say that your have unexpected and interesting results if the data were interpreted in a certain way, and speculate on the implications. But to actually insert new hypotheses after the research was done seems too much like torturing data to yield the results you want. After all, didn't someone once said that if you torture data sufficiently, they can confess to anything?

But as I said, I am no expert on the matter, and have yet to start on the PhD journey. This is based on readings from a while ago, and I might not have recalled it properly.

Think I read an article somewhere that adding in a hypothesis post-hoc is bad practice, but I may have remembered wrongly. I am sure your supervisors would have better answers to your question.

The minimum requirements for a funded RC studentship is a strong 2:1 + a strong Merit, but its likely that you would need at least a First + Strong Merit, or preferably, a strong 2:1 + Distinction to have any realistic chance of getting funded, given the strong competition for funded places. Time to work hard in your Master's...:) BTW, you ought to hurry if you want to start in the 2018 academic year, deadline is Mid January for most RC funding applications.

The short answer to your question is: yes! It is hard to find funding these days, especially in the social sciences. We are talking in the region of 60K for a three year studentship, so you are expected to do some leg work to try and find that money, rather having it handed to you on a plate.

That said, I think your first port of call should be to your personal tutor and/or your director of research at your current uni. They can offer you the best advice to the funding process, and may even suggest opportunities at your present uni. You next port of call should be to contact suitable academics as potential supervisor at other unis, and talk to them about your interest, and also tell them that you are looking for funding. They should be also to tell how likely you are likely to get funding, if they are interested in supervising your topic. Here I am only talking about RC studentships, and individual funded projects are usually advertised on the websites that other posters have suggested.

Good luck with your quest.

Not sure about London based PhDs, but the average salary of PhDs in this country is certainly nowhere near the 47K mark.